Question

If isotopic distribution of $C-12$ and $C-14$ is 98 % and 2 % respectively, what would be the number of $C-14$ isotope in $12gm$ carbon sample?

• A. $1.032\times {10}^{22}$
• B. $3.01\times {10}^{23}$
• C. $5.88\times {10}^{23}$
• D. $6.02\times {10}^{23}$

Answer 1

The correct option is A $1.032\times {10}^{22}$

1 mole of carbon contains $N_A$ molecules.

$14g$ of $C-14$ contains $6.023\times {10}^{23}$ atoms

$1g$ of $C-14=\frac{6.023\times {10}^{23}}{14}$

$12g$ of $C-14$ atom contains $=\frac{6.023\times 10623\times 12}{14}$

$=5.16\times {10}^{23}$ atoms

Now $2$% of $5.16\times {10}^{23}=\frac{5.16\times {10}^{23}\times 2}{100}$

$=1.032\times {10}^{22}$ atoms .